Editing Linear particle accelerator (section)

==Basic principles of operation==

[[Image:Linear accelerator animation 16frames 1.6sec.gif|thumb|upright=2.5|Animation showing how a linear accelerator works.  In this example the particles accelerated (red dots) are assumed to have a positive charge.  The graph ''V''(x) shows the [[electrical potential]] along the axis of the accelerator at each point in time.  The polarity of the RF voltage reverses as the particle passes through each electrode, so when the particle crosses each gap the electric field ''(E, arrows)'' has the correct direction to accelerate it.  The animation shows a single particle being accelerated each cycle; in actual linacs a large number of particles are injected and accelerated each cycle.  The action is shown slowed enormously.]]

<div style="clear: both"></div>
=== Radiofrequency acceleration ===

When a [[charged particle]] is placed in an [[electromagnetic field]] it experiences a force given by the [[Lorentz force]] law:

:<math>\vec{F} = q \vec{E} + q \vec{v} \times \vec{B}</math>

where <math>q</math> is the charge on the particle, <math>\vec{E}</math> is the electric field, <math>\vec{v}</math> is the particle velocity, and <math>\vec{B}</math> is the magnetic field. The cross product in the magnetic field term means that static magnetic fields cannot be used for particle acceleration, as the magnetic force acts perpendicularly to the direction of particle motion.<ref name="conte">{{cite book |last1=Conte |first1=Mario |last2=MacKay |first2=William |title=An introduction to the physics of particle accelerators |date=2008 |publisher=World Scientific |location=Hackensack, N.J. |isbn=9789812779601 |pages=1 |edition=2nd}}</ref>

As [[Electrical breakdown|electrostatic breakdown]] limits the maximum constant voltage which can be applied across a gap to produce an electric field, most accelerators use some form of RF acceleration. In RF acceleration, the particle traverses a series of accelerating regions, driven by a source of voltage in such a way that the particle sees an accelerating field as it crosses each region. In this type of acceleration, particles must necessarily travel in "bunches" corresponding to the portion of the oscillator's cycle where the electric field is pointing in the intended direction of acceleration.<ref name="edwards">{{cite book |last1=Edwards |first1=D. A. |last2=Syphers |first2=M.J. |title=An introduction to the physics of high energy accelerators |date=1993 |publisher=Wiley |location=New York |isbn=9780471551638}}</ref>

If a single oscillating voltage source is used to drive a series of gaps, those gaps must be placed increasingly far apart as the speed of the particle increases. This is to ensure that the particle "sees" the same phase of the oscillator's cycle as it reaches each gap. As particles asymptotically approach the speed of light, the gap separation becomes constant: additional applied force increases the energy of the particles but does not significantly alter their speed.{{r|conte|p=9-12}}

=== Focusing ===
In order to ensure particles do not escape the accelerator, it is necessary to provide some form of focusing to redirect particles moving away from the central trajectory back towards the intended path. With the discovery of [[strong focusing]], [[quadrupole magnets]] are used to actively redirect particles moving away from the reference path. As quadrupole magnets are focusing in one transverse direction and defocusing in the perpendicular direction, it is necessary to use groups of magnets to provide an overall focusing effect in both directions.{{r|conte}}

====Phase stability====
Focusing along the direction of travel, also known as ''phase stability'', is an inherent property of RF acceleration. If the particles in a bunch all reach the accelerating region during the rising phase of the oscillating field, then particles which arrive early will see slightly less voltage than the "reference" particle at the center of the bunch. Those particles will therefore receive slightly less acceleration and eventually fall behind the reference particle. Correspondingly, particles which arrive after the reference particle will receive slightly more acceleration, and will catch up to the reference as a result. This automatic correction occurs at each accelerating gap, so the bunch is refocused along the direction of travel each time it is accelerated.{{r|edwards|pp=30-52}}